Is it inappropriate for my boyfriend to go bike riding alone with a girl that wants to date him?

There is a girl that was steadily trying to date my boyfriend before we got together. In fact, when we started dating, she called and cursed him out for being an because he started dating me and not her. Well, he's training for a triathlon now and, amazingly, so is she and she wants to go bike riding alone with him... He doesn't think anything us wrong with that because he is not interested in her "in that way". Am I wrong for thinking this is completely inappropriate and disrespectful to our relationship??